John F. Kelly, President Trump’s new chief of staff, is focused on ending chaos in the White House. Given that his boss is the self-disrupter in chief, good luck with that.

And Trump world’s vicious backstabbing is not, in any event, the administration’s most important problem. A devotion to lying is a far graver danger to this presidency, and military efficiency will not dispel it.

The Post’s report, essentially confirmed by the White House, that the president was the prime mover behind Donald Trump Jr.’s misleading statement about his meeting with a Russian lawyer peddling derogatory information about Hillary Clinton ratifies the pattern of deceit and misdirection on all matters Russian. Behaving as if you are guilty won’t convince others that you are innocent.

The president seems convinced that he can survive whatever comes his way as long as he keeps his much-celebrated political base with him. But this is not as easy as it sounds for either Trump or his party because his base is fundamentally divided.

Nothing illustrated this more dramatically than the health-care showdown. Trump’s rhetoric about the Affordable Care Act during last year’s campaign should have been a tipoff to the dilemma both he and conservative politicians confront now. On the one hand, he roundly denounced Obamacare, which made right-wing ideologues happy. But he also regularly promised an alternative that would be more, not less, generous in helping Americans of modest means.

(Dalton Bennett,Kate Woodsome/The Washington Post)

His position was incoherent but very shrewd. To pull off his electoral college victory in 2016, Trump needed the votes of traditional Republican conservatives, but he also had to add on non-ideological working-class voters, many of whom found Mitt Romney unappealing in 2012.

For clues about the political turmoil and coalition-management challenges the president and the GOP face, consult “The Five Types of Trump Voters” by Emily Ekins, the director of polling at the Cato Institute. The bottom line of her research is that Trump and his party can’t win without the conservative faithful, but the conventional right alone cannot guarantee victory.

A narrow majority of Trump’s voters, Ekins found, fell into two traditionally Republican groups, “Staunch Conservatives,” who made up 31 percent of his backers, and “Free Marketeers,” who constituted 25 percent. She also identifies a smaller, less loyally Republican faction, “The Disengaged,” who amounted to 5 percent of his supporters.

But two other large Trump groups, whom Ekins labeled “American Preservationists” (20 percent of Trumpists) and “Anti-Elites” (19 percent), are quite different from regular conservatives. In particular, Ekins notes, both “lean economically progressive,” which is why the health-care issue is so problematic for Trump.

The preservationists might be seen as White House adviser Stephen K. Bannon’s people. They “have nativist immigration views, and a nativist and ethnocultural conception of American identity.” The Anti-Elites are more moderate on these issues and the “most likely” of the Trump supporters “to favor political compromise.” This group was never as strongly pro-Trump as the others, and seems most ripe for defection to the Democrats.

Trump is so hungry for “wins” that he is still pushing the Senate to pass any bill to repeal Obamacare. But enacting proposals along the lines of those that failed last week would be the worst possible outcome for Trump because they effectively break the promises he made to nearly 40 percent of his own sympathizers.

Senate Republicans who want to back away from repeal, at least for now, seem more attuned to how disruptive this issue is. But the looming battle over deep tax cuts tilted toward the wealthy will also split the alliance Trump is counting on for survival.

As Ekins concludes, Trump voters “hold different perceptions of justice in the political and economic systems.”

Trump’s coalition is by no means unique historically in bringing together constituencies with widely divergent views. Franklin D. Roosevelt, after all, won votes from Northern African Americans and Southern white segregationists. On the other hand, the New Deal alignment was shattered when civil rights became a driving national issue.

Still, political leaders trying to hold diverse groups together need to demonstrate finesse and both the appearance and reality of successful governance. Finesse, needless to say, is not a Trump long suit. And every day that brings a new Trump revelation, new questions about Russia or sheer craziness (the Mooch interlude or the president’s reported description of the White House as “a real dump”) puts increased pressure on a rickety alliance that can only bear so much. When Trump most needs that base of his, it may no longer be there.